The optimal design of laminated plates for maximum buckling load using finite element and analytical methods.

Abstract

In the first part of the study, finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates subject to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximisation of the biaxial buckling load by determining the fibre orientations optimally with the effects of bending-twisting coupling taken into account. The finite element method coupled with an optimisation routine is employed in analysing and optimising the laminated plate designs. The effect of boundary conditions, the number of layers and bending-twisting coupling on the optimal ply angles and the buckling load are numerically studied. Optimal buckling designs of symmetrically laminated rectangular plates under in-plane uniaxial loads which have a nonuniform distribution along the edges are presented in the second part of the study. In particular, point loads, partial uniform loads and nonuniform loads are considered in addition to uniformly distributed in-plane loads which provide the benchmark solutions. Poisson's effect is taken into account when in-plane restraints are present along the unloaded edges. Restraints give rise to in-plane loads at unloaded edges which lead to biaxial loading, and may cause premature instability. The laminate behavior with respect to fiber orientation changes significantly in the presence of Poisson's effect as compared to that of a laminate where this effect is neglected. This change in behavior has significant implications for design optimisation as the optimal values of design variables with or without restraints differ substantially. In the present study, the design objective is the maximisation of the uniaxial buckling load by optimally determining the fiber orientations. Numerical results, determined using the finite element method, are given for a number of boundary conditions and for uniformly and non-uniformly distributed buckling loads. In the third part of the study, finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates with central circular cut-outs subject to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximisation of the biaxial buckling load by determining the fiber orientations optimally. The effect of boundary conditions and bending-twisting coupling on the optimal ply angles and the buckling load are numerically studied. The results are compared to those for laminates without holes. The fourth part of the present study gives optimal designs of symmetrically laminated angle-ply plates, which are obtained with the objective of maximising the initial post buckling stiffness. The design involves optimisation over the ply angles and the stacking sequence to obtain the best laminate configuration. The stacking sequence is chosen from amongst five candidate designs. It is shown that the best configuration depends on the ratio of the in-plane loads in the x and y directions. Results are also given for two additional configurations which do not exhibit bending-twisting coupling. The final section of the present study deals with the optimal design of uniaxially loaded laminated plates subject to elastic in-plane restraints along the unloaded edges for a maximum combination of prebuckling stiffness, postbuckling stiffness and buckling load. This multiobjective study illustrates that improved buckling and post buckling performance can be obtained from plates which are designed in this fashion. The multiobjective results are also compared to single objective design results.